Constantin Carathéodory was born on 13 September 1873 in Berlin to Greek parents. His father was a diplomat. Carathéodory attended École Militaire de Belgique and École d'Application in Belgium, training to be an engineer. Afterwards he worked as an engineer for the British Colonial Service in Egypt, and it was at this point that he began, on his own, a serious study of mathematics. In 1900 he left the Colonial Service and began graduate studies in mathematics at the University of Berlin and then the University of Göttingen, where he received the PhD degree in 1904. Carathéodory held academic positions at the University of Berlin, the University of Göttingen, the Ionian University of Smyrna, and the University of Munich. He died on 2 February 1950 in Munich.
Carathéodory made important contributions in the calculus of variations, real analysis, complex analysis, and measure theory. To students of measure theory (and probability) he is best known for the theorem that guarantees the extension of a measure from an algebra to a \( \sigma \)-algebra, now known as the Carathéodory extension theorem in his honor.